This chapter describes the functions for generating random variates and computing their probability densities provided by the PLT Scheme Science Collection/

The functions described in this chapter are defined in the random-distributions sub-collection of the science collection. All of the modules in the random-distributions sub-collection can be made available using the form:

Returns a pair of correlated Gaussian variates, with mean 0, correlation coefficient rho, and standard deviations sigma-x and sigma-y in the x and y directions using the random source s or (current-random-source) if s is not provided. The correlation coefficient rho must lie between -1 and 1.

Example: 2D histogram of random variates from the bivariate Gaussian distribution with standard deviation 1.0 in both the x and y direction and correlation coefficient 0.0.

7.2.2Bivariate Gaussian Distribution Density Functions

Computes the probability density, p(x, y), at (x, y) for the bivariate gaussian distribution with mean 0, correlation coefficient rho, and standard deviations sigma-x and sigma-y in the x and y directions.

7.2.3Bivariate Gaussian Distribution Graphics

The bivariate Gaussian distribution graphics are defined in the "bivariate-gaussian-graphics.ss" file in the random-distributions sub-collection of the science collection and are made available using the form:

Returns a plot of the probability density and cumulative density of the bivariate Gaussian distribution with mean 0, correlation coefficient rho, and standard deviations sigma-x and sigma-y in the x and y directions. The plot is produced by the plot collection provided with PLT Scheme.

Example: Plot of the probability density and cumulative density of the bivariate Gaussian distribution mean 0, correlation coefficient 0.0, and standard deviations 1.0 and 1.0 in the x and y directions.

7.8.1Random Variates from the Gaussian (Normal) Distribution

Returns a random variate from the Gaussian (normal) distribution with mean mu and standard deviation sigma using the random source s or (current-random-source) if s is not provided. This function uses the Box-Mueller algorithm that requires two calls to the random source s.

Returns a random variate from the Gaussian (normal) distribution with mean 0.0 and standard deviation 1.0 using the random source s or (current-random-source) if s is not provided. This function uses the Box-Mueller algorithm that requires two calls to the random source s.

Returns a random variate from the Gaussian (normal) distribution with mean mu and standard deviation sigma using the random source s or (current-random-source) if s is not provided. This function uses the Kinderman-Monahan ratio method.

Returns a random variate from the Gaussian (normal) distribution with mean 0.0 and standard deviation 1.0 using the random source s or (current-random-source) if s is not provided. This function uses the Kinderman-Monahan ratio method.

Returns a plot of the probability density and cumulative density of the Gaussian (normal) distribution with mean mu and standard deviation sigma. The plot is produced by the plot collection provided with PLT Scheme.

Example: Plot of the probability density and cumulative density of the Gaussian (normal) distribution with parameters mean 10.0 and standard deviation 2.0.

7.9.1Random Variates from the Gaussian Tail Distribution

Returns a random variate from the upper tail of the Gaussian distribution with mean mu and standard deviation sigma using the random source s or (current-random-source) if s is not provided. The value returned is larger than the lower limit a, which must be greater than the mean mu.

Example: Histogram of random variates from the upper tail greater than 16.0 of the Gaussian distribution with mean 10.0 and standard deviation 2.0.

Returns a random variate from the upper tail of the Gaussian distribution with mean 0 and standard deviation 1 using the random source s or (current-random-source) if s is not provided. The value returned is larger than the lower limit a, which must be greater than the mean mu.

Returns a plot of the probability density and cumulative density of the upper tail greater than a of the Gaussian distribution with mean mu and standard deviation sigma. The plot is produced by the plot collection provided with PLT Scheme.

Example: Plot of the probability density and cumulative density of the upper tail greater than 16.0 of the Gaussian distribution with parameters mean 10.0 and standard deviation 2.0.

Returns a plot of the probability density and cumulative density of the upper tail greater than a of the unit Gaussian distribution. The plot is produced by the plot collection provided with PLT Scheme.

Example: Plot of the probability density and cumulative density of the upper tail greater than 3.0 of the unit Gaussian (normal) distribution.

Returns a plot of the probability density and cumulative density of the log normal distribution with mean mu and standard deviation sigma. The plot is produced by the plot collection provided with PLT Scheme.

Example: Plot of the probability density and cumulative density of the log normal distribution with mean 0.0 and standard deviation 1.0.

Returns a plot of the probability density and cumulative density of the triangular distribution with minimum value a, maximum value b, and most likely value c. The plot is produced by the plot collection provided with PLT Scheme.

Example: Plot of the probability density and cumulative density of the triangular distribution with minimum value 1.0, maximum value 4.0, and most likely value 2.0.